Exploring the asymmetric effect of COVID-19 pandemic news on the cryptocurrency market: evidence from nonlinear autoregressive distributed lag approach and frequency domain causality

This paper explores the asymmetric effect of COVID-19 pandemic news, as measured by the coronavirus indices (Panic, Hype, Fake News, Sentiment, Infodemic, and Media Coverage), on the cryptocurrency market. Using daily data from January 2020 to September 2021 and the exponential generalized autoregressive conditional heteroskedasticity model, the results revealed that both adverse and optimistic news had the same effect on Bitcoin returns, indicating fear of missing out behavior does not prevail. Furthermore, when the nonlinear autoregressive distributed lag model is estimated, both positive and negative shocks in pandemic indices promote Bitcoin’s daily changes; thus, Bitcoin is resistant to the SARS-CoV-2 pandemic crisis and may serve as a hedge during market turmoil. The analysis of frequency domain causality supports a unidirectional causality running from the Coronavirus Fake News Index and Sentiment Index to Bitcoin returns, whereas daily fluctuations in the Bitcoin price Granger affect the Coronavirus Panic Index and the Hype Index. These findings may have significant policy implications for investors and governments because they highlight the importance of news during turbulent times. The empirical results indicate that pandemic news could significantly influence Bitcoin’s price.


Wavelet Quantile Correlation
Bitcoin have shown long-term diversifier features but no safe haven characteristics for a highly market capitalized index like the S&P500 Maitra et al. (2022) August 1, 2019,-May 29, 2020 Bitcoin, Ethereum, eight stock market indices Copula-based VaR and CoVaR models Cryptocurrencies are unable to generate additional earnings by reducing stock market risk in the face of the COVID-19 pandemic Omane-Adjepong and Alagidede  Karaömer (2022) confirmed that throughout the prominent incidents, cryptocurrency policy uncertainty (UCRY Policy) has a detrimental effect on digital currency returns, suggesting that they are ineffective as a hedge or safe-haven asset. By investigating the initial equities bear market related to the pandemic,  reported that Bitcoin and Ethereum are not a safe-haven for most of the explored global equity markets because their integration increased portfolio downside risk. López−Cabarcos et al. (2021) suggested that Bitcoin can be considered a safe-haven during turbulent periods but is desirable for speculative investors during stable terms. Furthermore, Arouxet et al. (2022) also questioned the viability of cryptocurrencies as a safe-haven during the disease outbreak because they were vulnerable to speculative moves, and significant shifts in volatility could indicate the uncertainty surrounding the real price. Hence, the phases of obvious bubble behavior (Corbet et al. 2018) and the doubting dealing operation (Gandal et al. 2018) may cast skepticism on Bitcoin's capability to serve as a safe-haven. According to Huang et al. (2021), the COVID-19 outbreak changed the role of Bitcoin globally, except for the United States, which may account for the conflicting results regarding the hedge and safe-haven status of cryptocurrencies in the pandemic era. Furthermore, Wang et al. (2019) proved that the safe-haven feature is more noticeable in developed markets and subgroups with greater market capitalization and liquidity. In this regard, Wüstenfeld and Geldner (2022) argued that Bitcoin acts differently based on the nation being investigated, highlighting the significance of country-level studies.

The effect of the COVID-19 pandemic on cryptocurrency returns
Due to low fundamental value, Mnif et al. (2022) proved that the major cryptocurrency markets experienced several short-lived bubbles during the coronavirus pandemic. Market stress increased belief dispersion, decreasing Bitcoin futures returns but significantly elevating volatility and trading volume in the pandemic phase compared to the pre-pandemic period (Park 2022). In contrast to the S&P 500 Index and gold, which usually alternated between 3 and 5%, Foley et al. (2022) found that the expected risk premium for Bitcoin is considerably higher than other markets, averaging around 80% yearly. Foroutan and Lahmiri (2022) reinforced that cryptocurrencies are more erratic and unstable than global stock markets during the COVID-19 pandemic. Furthermore, Benlagha and Hemrit (2022) suggested that high stock market risk aversion and fear increase the value of Bitcoin; however, Haffar and Fur (2022) asserted that, except for a bear market, no asset could impact Bitcoin because it is a solitary market.
Furthermore, another branch of studies explored the relationship between coronavirus figures and digital asset returns, finding contradictory outcomes. Table 2 provides a summary of prior literature in this regard. Although the COVID-19 pandemic harmed the economy, Lee et al. (2022) showed that it had no discernible impact on Bitcoin; hence, some earlier research supported the conclusion that there is no connection between COVID-19 and the cryptocurrency market. In this regard, apart from USDT, Minutolo et al. (2022) noticed that the spread variation of the entire world has no impact on the price return of the major cryptocurrencies. Kim and Orlova (2021) estimated multivariate regressions, finding that the pandemic occurrence barely affected the performance of Bitcoin futures. Havidz et al. (2022a) uncovered that the COVID-19 cumulative positive cases had positive but insignificant effects on Bitcoin returns. Additionally, Vukovic   COVID-19 had a beneficial impact on crypto returns Gherghina andSimionescu Financial Innovation (2023) 9:21 et al. (2021) discovered that the COVID-19 crisis had no statistically significant direct impact on the cryptocurrency market during the initial wave, and Fernandes et al. (2022) demonstrated that cryptocurrencies displayed significantly stable price dynamics both before and during the pandemic. Furthermore, Fareed et al. (2022), among other studies, reported a nonlinear relationship between COVID-19 and Bitcoin. Hou et al. (2021) also found a short-term negative effect of COVID-19 on Bitcoin prices but a long-term beneficial effect due to its features, such as digital payments, unbanked assets, and safer virus propagation. Marobhe (2022) proved that Bitcoin, Ethereum, and Litecoin all experienced sizable negative return shocks during the first wave of COVID-19; however, they bounced back in April 2020 and remained resilient to subsequent COVID-19 panic shocks.
By examining the closing prices of Bitcoin, Ripple, Litecoin, and Dash, Nitithumbundit and Chan (2022) reported greater return persistence, volatility, and cross-dependency during the disease outbreak, proving increased risk. Furthermore, Usman and Nduka (2022) observed a rise in persistence levels compared to before COVID-19 was declared a pandemic. Sui et al. (2022) confirmed that the cryptocurrency market was impacted by COVID-19, which substantially increased its total risk spillover effect. Similarly, Nguyen (2022) confirmed a volatility spillover effect from the stock market to Bitcoin throughout the pandemic phase and other times of extreme uncertainty. Abraham (2021) used an event study approach and noticed that around COVID-19 dates, both Bitcoin and Altcoins experienced negative abnormal returns, with Altcoins being more adversely impacted. According to Bashir and Kumar (2022), a 1% rise in the Google search volume index, Twitter economic uncertainty, and tweets leads to a reduction in Bitcoin returns of 0.44, 0.33, and 1.35%, respectively. Demir et al. (2020) identified a negative connection among Bitcoin value and the number of reported cases and deaths; however, the relationship turns into positive throughout the subsequent period. In this regard, Di and Xu (2022) argued that despite the increasing number of new COVID-19 cases brought on by Omicron, the vaccine boosted confidence and sped up the financial market recovery, significantly positively impacting the ability of the financial market to recover from the pandemic.
Other research suggested that the pandemic had a beneficial impact on cryptocurrency returns. According to Mzoughi et al. (2022), the performance of the digital gold-containing portfolio improved during the COVID-19 crisis, particularly in cumulative returns. Temkeng and Fofack (2021) noticed that new COVID-19 deaths strongly impacted the price of cryptocurrencies, but not by new confirmed cases, total cases, or total deaths. Goodell and Goutte (2021) confirmed that levels of COVID-19 instigated an increase in Bitcoin prices. Karamti and Belhassine (2021) found that the more US-COVID-19 fear increases, the more investors run to Bitcoin. Furthermore, Sarkodie et al. (2022) documented a mean daily surge in the market price of Ethereum, Bitcoin, Litecoin, and Bitcoin Cash by 0.58%, 0.44%, 0.36%, and 0.15%, respectively, when COVID-19 confirmed cases and deaths rose by 3.77%, and 3.65% daily. Similarly, Corbet et al. (2020) reported a significant increase in both returns and trading volumes, implying that sizable virtual currencies functioned as a store of wealth throughout this period of intense financial market tension.
Page 13 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 The nexus between pandemic news and the cryptocurrency market The increasing prevalence of the COVID-19 pandemic heightened pessimism in the world's leading markets ). An economic individual does not constantly act reasonably because their judgments are altered by beliefs . Poor tempers and distress may influence investor choices, such as tense individuals losing hope concerning upcoming returns, inclining them to take less risk (Kaplanski and Levy 2010). Positive feedback trading or trend chasing implies that investors buy securities when prices increase and sell when prices go down (Long et al. 1990), while negative feedback or contrarian trading implies buying after price decline (Cutler et al. 1990). King and Koutmos (2021) identified a discrepancy in trading design, namely trend chasing for Bitcoin, Ethereum, XRP, and Cardano, but contrarian trading for EOS and Stellar; hence, Agosto et al. (2022) proved that sentiment is crucial in early warning bubble signals.
Cryptocurrencies are renowned for their extreme volatility and long-term fluctuations brought on by investors' emotions; they are not traded on regulated markets and are not subject to the same regulations as traditional financial instruments (Assaf et al. 2022). Sentiment analysis is a widely researched field in the era of social media and has been employed to boost trading cryptocurrency estimations (Fang et al. 2022). Thus, the cryptocurrency market heavily mirrors media platforms, with high aspirations, quick swings in sentiment, definite opinions, and intense debates (Aste, 2019). Specifically, the use of emotion statistics obtained via social media and based on a glossary of words allows for evaluating opinions depending on the severity of the pandemic and the interconnections between such feelings and cryptocurrencies ). Bowden and Gemayel (2022) evidenced that emotion influences investors' decisions because bullish sentiment generates positive returns for cryptocurrency traders. Umar and Gubareva (2020) claimed that cryptocurrency markets are highly responsive to overall sentiment and vulnerable to mainline anticipations, particularly throughout crises such as the COVID-19 pandemic. The third strand of literature is oriented on how investor sentiments extracted from news, social networks such as Twitter, or investor attention from Google influence Bitcoin. Urquhart (2018) found that Google Trends, as a measure of investor attention, is affected by Bitcoin's previous day high realized volatility and volume. Shen et al. (2019) proved that the number of tweets on Twitter significantly drives Bitcoin's future realized volatility and trading volume. Kraaijeveld and Smedt (2020) confirmed that Twitter sentiment can be used to forecast the price returns of Bitcoin, Bitcoin Cash, and Litecoin, while Naeem et al. (2020) showed that Twitter Happiness Index is a significant predictor of Bitcoin, Ethereum, Ripple, Litecoin, and Monero, contingent on the market status. Huynh (2021) noticed that more pessimistic Trump sentiments led to higher Bitcoin returns. Choi (2021) exhibited that the number of tweets positively influences Bitcoin liquidity. Contrariwise, Anastasiou et al. (2021) exhibited that investors' crisis sentiment proxied by the Financial and Economic Attitudes Revealed by Search index positively influences cryptocurrencies' market price crash risk. Besides, Sifat (2021) supported the detachment of cryptocurrencies' price, volatility, and trading operations from global sentiments over 2015−2021. Table 3 presents a brief review of the literature in this direction.
National uncertainty is essential in Bitcoin investors' decision-making since most of its related trading volume and holders are condensed in a few nations (Wu et al. 2021a). Elsayed et al. (2022) noticed that the volatility spillover of Bitcoin is driven by Economic Policy Uncertainty (EPU), but Twitter-based Economic Uncertainty does influence Bitcoin's volatility. Shaikh (2020) also confirmed a negative relationship between uncertainty in the equity market and Bitcoin returns, whereas EPU influences Bitcoin returns. Yen and Cheng (2021) documented that a variation in the China EPU is negatively connected with the future volatility of Bitcoin and Litecoin. Conversely, Cheng and Yen (2020) claimed that China's EPU index predicts Bitcoin returns, but the US, Japanese, and Korean EPU indexes do not. Mokni (2021) noticed that EPU could forecast volatility merely when the Bitcoin market is bullish.
Behavioral finance has exposed a range of preconceptions that affect investment judgments (Shrotryia and Kalra, 2021). Banerjee (1992) argued that individuals would follow others instead of utilizing their knowledge. Youssef and Waked (2022) proved that media could influence investors' behavior regarding the coronavirus, causing them to ignore their personal information and replicate other people's investment choices. As such, Jia et al. (2022) asserted that investor sentiment and herding behaviors are connected. According to Sapkota (2022), emotions have a medium-term effect on Bitcoin fluctuation, while financial viewpoints have a longterm influence. For instance, Wang et al. (2022) found that throughout the COVID-19 pandemic, market insecurity triggered by contagious illnesses contributes to a positive feedback trading mentality. Hence, the fourth stream of literature focuses on investors' different biases. Gurdgiev and O'Loughlin (2020) noticed a surge in cryptocurrency prices when there prevails positivity among investors, thus suggesting the occurrence of herding biases. Mandaci and Cagli (2021) detected intensified herding conduct during the coronavirus outbreak, whereas Rubbaniy et al. (2021) confirmed herd investing after the relaxation of the isolation measures. According to Ferreruela and Mallor (2021), during the COVID-19 disease outbreak, herding is evidenced on days with high volatility. Furthermore, Kyriazis (2020) highlighted that bull markets can cause more severe herding than bear markets, contributing to biases. Anamika and Subramaniam (2022) supported that the cryptocurrency market exhibits herding conduct when the sentiment of investors is upbeat or bullish, which increases prices. Kakinaka and Umeno (2021a) claimed that COVID-19 enhanced herding in the short-term, but not in the long-term; however, Mnif and Jarboui (2021) claimed that the pandemic has lessened the herd bias. Moreover, Güler (2021) highlighted the FOMO behavior illustrated by the fear a Bitcoin investor encounters when overlooking a potentially profitable investment or trading opportunity.
Several features emerge from the preceding literature. First, there has been a heated debate about cryptocurrencies' diversifier, hedge, and safe heaven qualities. Second, the literature regarding the impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on cryptocurrency returns reported conflicting results. Third, various proxies for investor sentiment proved to be significant drivers of Bitcoin price. Finally, most research findings reported an expansion of herding behavior throughout the pandemic period.

Data and variables
Our dataset consists of daily Bitcoin returns, COVID-19-related news measures, coronavirus figures, and the VIX index from January 2020 to September 2021. Table 4 shows the definitions of the whole covered variables. We selected Bitcoin as a proxy for the cryptocurrency market since it is the primary, largest-capped (Raza et al. 2022b), and most prominent virtual currency (Anamika et al. 2021;Tiwari et al. 2019), recognized as a substitute payment method by many traders (Feng et al. 2018;Burggraf et al. 2021;Diaconaşu et al. 2022;Karaömer, 2022). According to Sebastião and Godinho (2021), Bitcoin's "ecosystem" possesses many characteristics, including immateriality, decentralization, accessibility, and consensualness. It is also integer-based, transparent, worldwide, quick, affordable, irreversible, immutable, divisible, resilient, and pseudonymous. Bitcoin's underlying technology, blockchain, also has several benefits, including distributed ledger, decentralization, information transparency, tamper-proof design, and openness (Xu et al. 2019). In line with Chen et al. (2022), Mahdi and Al-Abdulla (2022), and Banerjee et al. (2022), we obtained coronavirus indices from RavenPack. RavenPack Coronavirus Media Monitor synthesizes the feelings (mood) expressed in news reports and public posts, which are then converted into convenient metrics (Rahadian and Nurfitriani 2022). The Coronavirus Panic Index is calculated by dividing the daily count of unique stories concerning panic key phrases and coronavirus by the daily number of  (2021) (2022), Havidz et al. (2022a), and Temkeng and Fofack (2021). According to Trichilli and Abbes (2022), COVID-19 data serve as a valuable device permitting forecasting of returns of cryptocurrencies, commodities, and stock markets. Following the extant literature, the VIX index was included to measure US market uncertainty (Sabah 2020;López-Cabarcos et al. 2021;Gaies et al. 2021;Chen et al. 2020;Smales, 2022;Anamika et al. 2021;Akyildirim et al. 2020;Gök et al. 2022;Dias et al. 2022;Minutolo et al. 2022). Su et al. (2022) considered that Bitcoin oscillations might be influenced by market concern, as assessed by the VIX, while Elsayed et al. (2022) found that Bitcoin usually received returns spillover from the VIX. Bouri et al. (2017) argued that greater values of the VIX imply more market insecurity and vice-versa. According to Smales (2022), volatility in US markets is critical to worldwide stock market insecurity, even if fluctuations in international market uncertainty do not explain shifts in US market turmoil. Furthermore, because the VIX information is a valuable resource for stockholders, it is essential to incorporate the VIX in any study of Bitcoin's power to hedge or its connection with other assets (Bouri et al. 2017).

Asymmetric GARCH framework toward cryptocurrency market volatility
Cryptocurrency market volatility is foremost for investors who intend to incorporate digital currencies in their portfolios (Gkillas et al. 2022). To seize the uneven influence triggered by adverse and optimistic news on the variance of Bitcoin, we consider the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model suggested by Nelson (1991). The selection of the EGARCH (1,1) model is based on the findings of Naimy and Hayek (2018), who showed the superiority of this specification over the symmetric GARCH (1,1) and exponentially weighted moving average. According to Haroon and Rizvi (2020), the EGARCH model outperforms other specifications due to its ability to permit more stable routine optimization and the lack of parameter restrictions. Furthermore, Güler (2021) found that the EGARCH (1,1) model is the most suitable. The volatility dynamics of the EGARCH (1,1) model are depicted below: where β signifies the persistence parameter, and α and γ describe the size and the sign (leverage) effect, respectively. If γ = 0, the model is entirely symmetric. If γ < 0, adverse shocks boost the instability more than positive shocks. For instance, Chen and Hafner (2019) confirmed that the volatility of Cryptocurrency IndeX (CRIX) soars as the Stock-Twits sentiment falls. According to Bashir and Kumar (2022), the volatility of the selected cryptocurrencies soars with increased investor focus and unease brought on by pandemic panic. If γ > 0, positive shocks raise the unpredictability more than adverse shocks (Güler 2021;Tiwari et al. 2019). Equation (1) presumes that error terms are normally distributed with a mean equal to 2 π (Naimy and Hayek 2018).

The nonlinear ARDL bounds testing approach for cointegration
Because market participants obtain information at different moments or interpret situations and facts diversely (Ante 2020), the asymmetric effect must be investigated to gain a better understanding of Bitcoin throughout the pandemic; this approach follows Iqbal et al. (2021), Apergis (2021), and Gaies et al. (2021). As such, Bourghelle et al. (2022) asserted that Bitcoin variability and sentiments may interfere with some asymmetry, complexity, and irregularity. Cheikh et al. (2020) also claimed that substantial price shifts, such as the December 2013 market crash and the late 2017 price levels, highlight the need to investigate whether asymmetric behavior occurs. For instance, Tiwari et al. (2019) demonstrated that digital currencies' volatilities react more to adverse shocks than positive ones. Fasanya et al. (2022) claimed that nonlinearity is essential for evaluating how investor sentiment influences the interplay between the markets for precious metals and cryptocurrencies. Long et al. (2021) found that when uncertainty lowers, the increase in Bitcoin price outweighs the decline when uncertainty increases. Yarovaya et al. (2021) found asymmetry in herding on bullish and bearish market days, implying panic-forced herding on days when the cryptocurrency market's value plummeted dramatically. Dias et al. (2022) reported that the consistency of investor sentiment fluctuates across market quantiles, indicating a nonlinear association. Consequently, in line with Iqbal et al. (2021), the variations in the regular number of recently reported COVID-19 instances and fatalities worldwide may influence the returns of Bitcoin differently. Choi and Shin (2022) argued that a shock mainly justifies the increase in Bitcoin prices to its price; however, other shocks, such as the VIX and projected inflation, generally support the drop.
Even if some previous studies estimated the long-and short-run relations (Béjaoui et al. 2021;Ciaian et al. 2016), the asymmetric associations were not assumed. To this end, we apply the NARDL model as in prior studies (Gaies et al. 2021;Rajput et al. 2020;González et al. 2021;Benlagha and Hemrit, 2022). The NARDL model is an asymmetric extension of the ARDL approach. The conventional unrestricted error correction model in the linear ARDL model proposed by Pesaran et al. (2001) is presented as follows: where Δ is the first difference operator, y t is the dependent variable, μ signifies the intercept, and x t is a k × 1 vector of regressors. ρ and θ correspond to the long-run coefficients, α j and π j denote the short-run coefficients, p and q depict the lag orders for the dependent and explanatory variables, and ε t is the error term. Following Shin et al. (2014), the nonlinear cointegration regression is described below: where u t is a stationary zero-mean error process that indicates deviations from the longrun equilibrium, and β + and β − denote the asymmetric long-run parameters. x t is the vector of regressors decomposed as follows: where x 0 is a random preliminary value. x + t and x − t depict partial sums of positive and negative changes in x t as follows: By associating Eq. (3) with the linear ARDL(p,q) model in Eq. (2), the asymmetric error correction model can be specified as: where θ + = −ρβ + and θ − = −ρβ − , while π + j and π − j seize the positive and negative shortrun adjustments in the explanatory variable x t . (2) Page 24 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 Furthermore, several phases should be completed before estimating the NARDL model in Eq. (7). The first step is to ascertain through unit root tests that the included variables are not I (2). Second, the error correction model in Eq. (7) is estimated by traditional ordinary least squares. Third, the bounds test is performed to explore the asymmetric long-run connection among the levels of the seriesy t , x + t andx − t , by applying the F statistic suggested by Pesaran et al. (2001). The null hypothesis of no cointegration (ρ = θ + = θ − = 0) is assessed versus the alternative of cointegration (ρ≠ θ + ≠ θ − ≠ 0). The fourth step consists of exploring the long-run (θ + = θ − ) and short-run (π + = π − ) asymmetries by means of the Wald test. Fifth, the asymmetric cumulative dynamic multiplier effect of a unit change in x + t and x − t on y t can be obtained as follows: For Eq. (8), as h → ∞, then m + h → β + and m − h → β − , where the asymmetric long-run coefficients β + = − θ + ρ and β − = − θ − ρ . The NARDL general model to be estimated in the context of our research takes the following form: where BTC t denotes the daily changes of Bitcoin price in period t. COVID_NEWS t depict each RavenPack coronavirus-related indices (Panic, Hype, Fake News, Sentiment, Infodemic, and Media Coverage) in period t, and COVID_CASES t signifies the daily number of newly reported COVID-19 cases and deaths worldwide in period t. VIX t indicates the daily change of the Chicago Board Options Exchange volatility index in period t, and ε t refers to the error term. Additionally, COVID_NEWS + , COVID_NEWS − , COVID_CASES + , COVID_CASES − , VIX + , and VIX − denote the partial sums of positive and negative fluctuations in the explanatory variables.

Causality analysis in the frequency domain
The magnitude and direction of causality vary among frequency bands (Granger and Lin 1995), but most conventional approaches to Granger causality disregard the probability that the association's intensity and path differ over various frequencies (Lemmens et al. 2008). We employ the frequency domain causality test developed by Breitung and Candelon (2006) to examine the causal connection between Bitcoin Page 25 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 returns and RavenPack coronavirus-related indices. The effectiveness of using this method ensues from its usage across all periodicities. Following Geweke (1982), a bivariate vector of time series is considered, z t = [x t , y t ] ′ , observed at time t = 1, …., T, with a finite-order vector autoregression representation, such as: where �(L) = I-1 L-…p L p is a 2 × 2 lag polynomial with L k z t = z t−k . The residual ε t is white noise with E(ε t ) = 0 and E(ε t ε ′ t ) = Σ. Since Σ is positive definite and symmetric, the Cholesky decomposition G ′ G = −1 occurs, where G is the inferior triangular matrix and G ′ is the upper triangular matrix, such that E(η t η ′ t ) = I and η t = G ε t . If the system (9) should be stationary, its moving average (MA) description is as follows: where �(L) = Θ (L) −1 and �(L) = �(L)G −1 . Using this representation, the spectral density of x t can be expressed as below: Furthermore, Geweke (1982) and Hosoya (1991) suggested the following measure of causality: If � 12 e −iω 2 = 0, then M y→x (ω) = 0, implying that y does not Granger cause x at periodicity ω; hence, the formulation of � 12 e −iω 2 = 0, can be rendered a state for the absence of Granger causality at frequency ω.
If the elements of z t are I(1) and cointegrated, then, in the frequency domain, the measure of causality can be specified by using the orthogonalized MA description as follows: where ψ (L) = ˜ (L)G −1 , η t = G ε t , and G is a lower triangular matrix, such that E(η t η ′ t ) = I. According to Engle and Granger (1987), in a bivariate cointegrated system, β ′ ψ(1) = 0, β is a cointegration vector, while β ′ z t is stationary. As in the stationary situation, the subsequent causality measure is exhibited as follows: The null hypothesis of y does not Granger cause x is formulated as follows: Breitung and Candelon (2006) exhibited this test by reshaping the association between x and y in a VAR equation as follows: The null hypothesis by Geweke (1982), M y→x (ω) = 0 , equates to the following null hypothesis: where β is the vector of the coefficients of y and This null hypothesis ∀ω ∈ (0, π) is tested by an ordinary F statistic distributed as F(2, T-2p), where 2 is the number of restrictions, p is the lag length of the VAR model, and T is the number of observations. Table 5 presents the basic statistics for all the time series. During the sample period, results show that the highest mean value is registered by Coronavirus Media Coverage Index, whereas Coronavirus Sentiment Index observes the lowest. The mean and median Bitcoin returns are positive, respectively, at 0.5396 and 0.3400%. In line with Wu et al. (2021a), the standard deviation of Bitcoin returns is 4.6169%, suggesting notably high volatility. Furthermore, Aste (2019) documented that prices and sentiment statistics are noisy with substantial volatility. The largest price decline is − 38.18%, and the greatest price rise is 19.56%. The skewness and kurtosis further display the asymmetric and highly leptokurtic distribution of returns. The Jarque−Bera test rejects the normality for all data series following Karaömer (2022). The non-normality of crypto market returns distributions exhibits the rejection of the efficient market assumption, even in its weak form, consistent with Nair (2021). Figure 1 shows the daily evolution of the selected variables. The largest drop of 38.18% in Bitcoin returns was registered on March 12, 2020, while the VIX's largest decline of 23.37% occurred on March 13, 2020. In the same vein, Akhtaruzzaman et al. (2022) reported that systemic risk soared significantly during the same period but fell to its lowest the subsequent day, suggesting that the advancement of systemic risk-sharing among virtual currencies adjusted rapidly. Mzoughi et al. (2022) ascertained that all markets displayed a substantial persistence in their volatility process, denoting the effects of the   Buigut and Kapar (2021), the correlation coefficients fluctuate extensively, varying from positive to negative. It can be argued that as pandemic cases changed over time, investors gained more knowledge about the disease, identified strategies to accommodate, and the mainstream press became insensitive. This finding is also in line  I  I I  I II  IV  I  I I  I II  2020 I  I I  I II  IV  I  I I  I II  2020  2021   II   20   40   60   80   100   I  I I  I II  IV  I  I I  I II  2020 I  I I  I II  IV  I  I I  I II  2020  2021   CND   0   20   40   60   80   100   I  I I  I II  IV  I  I I  I II  2020 Fig. 1 Variable trends from the sample period. Source Authors' own work. Notes: Variables' description is provided in Table 4 Page 29 2020), we estimate an EGARCH (1,1) model. Appendices 3 and 4 present the estimation outcomes for Bitcoin and VIX. Accordingly, since C(4) in Appendix 3 indicates that the leverage parameter is not statistically significant, we conclude that no asymmetric effect occurs for Bitcoin; hence, volatility does not rise more in reaction to positive shocks than in response to adverse shocks. The outcomes are in line with Wang (2021) and Nair (2021) (2021), and Bashir and Kumar (2022). Furthermore, Kakinaka and Umeno (2021b) and Cheikh et al. (2020) concluded that the asymmetric effect could not be statistically confirmed. According to Nair (2021), the profit (deficit) registered in the preceding period is quite significant in generating shortfalls (rewards) to dealers through the following day in both high-and low-price extreme shifts of crypto markets. Overall, the FOMO behavior identified in prior studies (Güler 2021; Baur and Dimpfl 2018) is not supported, suggesting that prudence rather than feelings drive the Bitcoin market; however, the empirical outcomes from Appendix 4 support that in the case of VIX the leverage effect is positive and statistically significant. This finding suggests that positive shocks can significantly impact volatility more than adverse ones. Cheikh et al. (2020) argued that investors seeking a hedge against a depressed stock market would transfer volatility and uncertainty to cryptocurrency markets throughout market tumult. Additionally, Fig. 2 exhibits that the conditional variance of VIX is greater than that of Bitcoin.

Stationarity investigation
Appendix 5 reveals the outcomes of stationarity tests performed with the traditional methods. The NARDL model is estimated regardless of whether the variables are integrated of order 0 or 1 (I(0) or I (1) considered if one of the variables is I(2) since the value of the F-test related to the bounds testing cointegration approach is invalid. We examine the order of integration between the variables through the ADF test proposed by Dickey and Fuller (1979) and the PP test suggested by Phillips and Perron (1988), following the extant literature (Polat et al. 2022;Mokni et al. 2022;Burggraf et al. 2021;Ghosh 2020;Sahoo 2021;Sahoo and Rath 2022). Furthermore, because the ADF and PP tests are supposed to be biased toward I(1) inferences, we employ the KPSS test of Kwiatkowski et al. (1992), in line with Kakinaka and Umeno (2021b), Sahoo (2021), and Karaömer (2022). Both ADF and PP tests rely on the null hypothesis that the variables comprise a unit root (follows a random walk) and therefore are not stationary, against the alternative hypothesis that a stationary process generated the data series; however, the KPSS test sets out as a null hypothesis that the variables are stationary. The results reveal that the variables are either I(0) or I(1), but none of the measures is stationary at the second difference, thus supporting the appropriateness of the NARDL model. Furthermore, the traditional stationarity tests may misleadingly establish that the variables are I(1) or I(2) when breaks occur in the series; therefore, we employ the test recommended by Zivot and Andrews (1992) to prove the rejection of I(2) measures. Appendix 6 provides the results of the ZA test. The outcomes reinforce that none of the variables is I(2), highlighting time breaks in the data, in line with Burggraf et al. (2021), Ghosh (2020), and Iqbal et al. (2021). Essentially, the identified breaks associate with the COVID-19 waves.

Checking for nonlinear dependence
To explore the likelihood of nonlinear dependence among Bitcoin returns and Raven-Pack coronavirus-related indices, we performed the Brock-Dechert-Scheinkman (BDS) test suggested by Broock et al. (1996). The BDS test is a nonparametric check robust to the structure of nonlinearity in the data. Table 6 shows the outcomes of the BDS test.
The BDS test rejects the null hypothesis of linearity consistent with Mokni et al. (2022), Raza et al. (2022a, b), namely independent and identically distributed residuals across various embedding dimensions. Therefore, all incorporated variables are nonlinear, proving the chaotic behavior in the time series data. Likewise, the nonlinear modeling approach is appropriate for this study's objectives.

Testing for cointegration
Next, we examine the cointegration link among the variables; Table 7 reports the results of the asymmetric cointegration test. The F-statistics are greater than the upper bound values involving the rejection of the null hypothesis of no cointegration; hence, the results show evidence for long-run relationships (cointegration) in all cases. Table 8 presents the estimates of NARDL models 1-6, covering the daily number of newly reported COVID-19 cases worldwide. Error correction term (ECT) is negative and statistically significant at 1%, thus confirming the ability of the short-run disequilibrium to adjust at long-run equilibrium. The long-term impact coefficients of the increase in the Coronavirus PI, Coronavirus Hype Index (HI), Coronavirus Fake Page 31 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 News Index (FNI), and Coronavirus Infodemic Index (II) on daily changes in Bitcoin price are 0.008191 (L + PI ), 0.000818 (L + HI ), 0.035054 (L + FNI ), and 0.001512 (L + II ), being statistically significant. This result shows that the rise in PI, HI, FNI, and II has a significant augmenting effect on Bitcoin returns; that is, when the PI, HI, FNI, and II rise by 1%, Bitcoin returns rise by 0.008191%, 0.000818%, 0.035054%, and 0.001512%, respectively. Additionally, the long-term impact coefficients of the decline in PI, HI, FNI, and II on Bitcoin returns are 0.007009 (L − PI ), 0.0007 (L − HI ) , 0.03341 (L − FNI ) , and 0.001215 (L + II ) , respectively, indicating that the decrease of PI, HI, FNI, and II significantly promotes Bitcoin's daily changes. The outcomes are in line with Rognone et al. (2020), suggesting investor fervor for Bitcoin regardless of the sentiment of the news. Furthermore, the positive impact of the pandemic sentiment on Bitcoin returns Table 6 Nonlinearity Brock-Dechert-Scheinkman (BDS) test Source Authors' own computations. Notes: Superscripts *, **, ***represent the significance at 10%, 5%, and 1% levels, respectively. Variables' description is provided in Table 4 Variables  Table 7 Bounds test for nonlinear cointegration Source Authors' own computations. Notes: Superscripts *, **, *** represent the significance at 10%, 5%, and 1% levels, respectively. Model selection method: Akaike info criterion (AIC). Variables' description is provided in Table 4 Model no Model specification NARDL specification F-statistic Critical Value  Source Authors' own computations. Notes: Superscripts * , ** , *** represent the significance at 10%, 5%, and 1% levels, respectively. The superscript + and -defines positive and negative partial sum. L + and L − are the computed long-run coefficients associated with positive and negative shocks, respectively. W LR denotes the Wald statistic for the long-run symmetry. W LR denotes the Wald statistic for the long-run symmetry, which tests the null hypothesis of θ + = θ − . X 2 SC denotes the Breusch-Godfrey Serial Correlation LM Test (first and second lag). X 2 HET denotes the Heteroskedasticity Test: ARCH (first and second lag). X 2 RESET denotes the Ramsey RESET Test of Misspecification. X 2 NORM denotes the Jarque-Bera test. The p-values of diagnostic tests are in []. Variables' description is provided in Table 4 Gherghina and Simionescu Financial Innovation (2023) 9:21 is consistent with Goodell and Goutte (2021). Additionally, Mahdi and Al-Abdulla (2022) showed that Bitcoin returns increase as the frequency of fear-related headlines increases. Following Shrotryia and Kalra (2021) and Marobhe (2022), the empirical findings reject any uneven behavioral shape throughout the pandemic disorder. The outcomes confirm Akhtaruzzaman et al. (2022), indicating that Bitcoin is systemically reliable and has a reduced potential to trigger structural disturbances. The quantitative outcomes also support Sifat (2021), who advocated dissociating digital currencies from global sentiments; however, the long-term impact coefficient of the decrease in Coronavirus Sentiment Index (SI) shows a negative influence on Bitcoin returns, whereas the long-run impact coefficient of the rise in SI is not statistically significant. With reference to the Coronavirus Media Coverage Index (MCI), the long-run impact coefficient of the increase in MCI is statistically significant, revealing a positive influence on daily changes of Bitcoin price. Additionally, the results of the Wald test show that the long-term asymmetric impact on Bitcoin returns is statistically significant only in the cases of PI and II.

NARDL outcomes
As for the daily number of newly reported COVID-19 cases worldwide, contrary to Sarkodie et al. (2022), the positive shock (L + CNC ) and negative shock (L − CNC ) , as shown in Table 8, are almost negative but not statistically significant. Furthermore, like Gaies et al. (2021), in the long-run, positive (L + VIX ) and negative (L − VIX ) shocks to VIX negatively impact Bitcoin returns at the 1% significance level. The outcomes are contrary to Anamika et al. (2021) but consistent with Bouri et al. (2016), who found that Bitcoin volatility inversely associates with US uncertainty, as well as Su et al. (2022).
Regarding the results of diagnostic tests of Table 8, Breusch-Godfrey serial correlation LM test ( χ 2 SC ) and ARCH heteroskedasticity test (χ 2 HET ) indicate that the null hypothesis (with no serial autocorrelation and heteroskedasticity in the residuals) cannot be rejected. Furthermore, in line with Gaies et al. (2021) and Rajput et al. (2020), the stability of the NARDL models 1-6 is checked and confirmed through the cumulative sum (CUSUM) and the CUSUM of squares (CUSUMQ) tests proposed by Brown et al. (1975) ; Fig. 3 presents the results. The CUSUM test provides a plot of the long-and short-term coefficients of the cumulative error terms of the number of observations with a 5% confidence interval, while the CUSUMQ test assesses the coefficients by squaring the cumulative error terms (Vurur 2021). The recursive and squared recursive residuals are drawn against breakpoints for CUSUM and CUSUMQ, respectively. If any point outstrips the 5% level of significance symbolized by the straight (red) lines, the null assumption that the parameters are stable is rejected (Gaies et al. 2021).
Generally, the blue lines do not outstrip the two red lines, suggesting that structural stability is supported for both short-and long-term estimates; hence, no significant structural variations compromise the stability of the estimates of the NARDL models. Figure 4 presents the NARDL multipliers for models 1-6 that exhibit the impact of positive and negative changes of VIX, the daily number of newly reported COVID-19 cases worldwide, and each RavenPack coronavirus-related indices on daily changes of Bitcoin price, following González et al. (2021) and Gaies et al. (2021). The horizontal axis depicts the period in days, and the vertical axis reveals the multiplier for positive (continuous black line) and negative (dashed black line) changes in VIX, CNC, each RavenPack coronavirus-related indices, and the asymmetry (dashed red line) with 95% Page 36 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 bootstrap confidence interval based on 1000 replications. If the 0 line is situated among the lower and upper bands, the asymmetric effects of the pandemic indices on Bitcoin are not significant at the 5% level. The plots exhibit a specific asymmetric adjustment of RavenPack measures to the equilibrium due to positive and negative shocks in the long-run. Except for Coronavirus SI, the plots reveal the dominance of positive coronavirus indices shocks. In the fourth model, positive change in the SI initially dominates negative change, but afterward, negative shocks dominate positive change.

Robustness check
To check the robustness of the quantitative outcomes, we re-estimate the NARDL models 1-6 by incorporating the daily number of newly reported COVID-19 deaths worldwide, following Iqbal et al. (2021) and Chen et al. (2022). Spiegel and Tookes (2021) argued the considerable differences in testing potential throughout time and territories, recommending centering on pandemic casualties rather than COVID-19 instances. Table 9 shows Bitcoin's related short-and long-run asymmetric dynamic interactions with RavenPack coronavirus-related indices. The coefficient of the ECT indicates that disequilibrium in the Bitcoin returns from the short-to long-run is adjusted by 111% and 113% annually. Concerning pandemic indices, only the coefficients related to Coronavirus PI, Coronavirus HI, and Coronavirus FNI are statistically significant. The estimated  (2021), a 1% increase or decrease in PI, HI, and FNI increases Bitcoin returns by 0.008382% (0.006814%), 0.00099% (0.00072%), and 0.03054% (0.028211%), respectively. The outcomes support Béjaoui et al. (2021), who claimed that the pandemic fosters investing in Bitcoin. Panic in the equity market appears to be driving investors to invest in Bitcoin as one of the alternative assets (Anamika et al. 2021). Like Guégan and Renault (2021), the significant association between investor sentiment and Bitcoin returns is supported; hence, the empirical findings reinforce Chen et al. (2022), indicating that Bitcoin is recognized as a valuable alternative investment under uncertainty. Contrary to Burggraf et al. (2021), an increase in market volatility does not lead to a flight-to-safety phenomenon. Contrary to Choi and Shin (2022), Bitcoin is largely unaltered by COVID-19 panic shocks. Thus, including Bitcoin in the portfolio can mitigate the risk of a sudden decline in the value of investments triggered by exogenous shocks such as COVID-19 (Marobhe, 2022). Like Diaconaşu et al. (2022), we may notice that the Bitcoin market tends to mature. Besides, the Wald test results reveal that long-run asymmetry effects are confirmed merely in the case of PI. Concerning the long-term positive (L + CND ) and negative (L − CND ) shocks of the daily number of newly reported COVID-19 deaths worldwide, the influence on daily changes of Bitcoin price is negative in most cases, but the statistical significance is weak. Furthermore, similar to the outcomes from Table 8, both positive and negative shocks of VIX significantly negatively impact Bitcoin returns in the long-run.
The diagnostic tests show that the estimated NARDL models 7-12 have no heteroskedasticity, serial correlation, or misspecification issues. Figure 5 illustrates that CUSUM and CUSUMSQ plots are within the 95% confidence level, denoting the stability of the estimated models.
After the positive and negative variations influencing Bitcoin, the adjustment of asymmetries from initial long-term equilibrium to new long-term equilibrium can be regarded via the dynamic multipliers reported in Fig. 6 for models 7-12. The coronavirus indices reveal asymmetric adjustment patterns toward negative and positive shocks in the short and long-run. Similar to adjustment patterns reported in Fig. 4, among the RavenPack pandemic indices, Coronavirus SI exhibits an inverse relationship with Bitcoin returns. In contrast, direct relationships between all other coronavirus measures and Bitcoin occur in both the short-and long-run.

Spectral causality analysis
The frequency domain causality analysis outcomes from pandemic indices to Bitcoin are reported in Table 10, whereas Fig. 7 shows the associated plots. The horizontal red lines in Fig. 7 signify the relationship between the variables at a 5% significance level for all frequencies (ω) in the interval (0, π) . Frequency (ω) on the horizontal axis can be interpreted as a cycle or periodicity by S = 2π/ω , where S is the period. Hence, high frequencies match short periods, and short frequencies relate to long periods. Unlike prior studies that used Twitter Happiness sentiment and found no Granger causality (Naeem et al. 2020(Naeem et al. , 2021b, the results support a long-term causal relationship running from Coronavirus FNI to Bitcoin, as well as a medium-term causal relationship from Coronavirus SI to Bitcoin. The outcomes support Mokni et al. (2022), who found an asymmetric causality only throughout the pandemic phase, and Polat et al. (2022), who reported that fear caused Bitcoin's return in the post-COVID era. Likewise, the findings align with Guégan and Renault (2021), who noticed that investor sentiment Granger causes Bitcoin returns. Furthermore, the outcomes are consistent with Zhu et al. (2021), suggesting that investor attention is a significant factor in the Bitcoin market. Additionally, Banerjee et al. (2022) proved a unidirectional causal relationship between COVID-19 news sentiment and cryptocurrency returns. However, the rest of RavenPack's coronavirus-related indices do not cause Bitcoin at any frequency range.  Bitcoin. Source Authors' own work. Notes: The incidence of the connection between each RavenPack coronavirus related indices and daily changes of Bitcoin price is investigated at frequencies 2-3, 1-2, and 0-1. These frequencies show a short, medium, and long-term relationship. 0-1 is established as permanent causality, while 2-3 is recognized as temporary causality. The (red) upper line and the (brown) lower line represent statistically significant levels of 5 and 10%, respectively. The (blue) curves are used for statistical tests of various interval frequencies (0, π). Variables' description is provided in Table 4 Page 44 of 58 Gherghina and Simionescu Financial Innovation (2023) 9:21 Table 11 shows the Breitung-Candelon spectral Granger causality test results from Bitcoin to pandemic indices, and Fig. 8 exhibits the related plots. The outcomes support that Bitcoin Granger causes Coronavirus PI for all frequencies. Significant Granger causality is also found from Bitcoin to Coronavirus HI in the medium and long-run. Source Authors' own work. Notes: The incidence of the connection between daily changes of Bitcoin price and each RavenPack coronavirus-related indices is investigated at frequencies 2-3, 1-2, and 0-1. These frequencies show a short, medium, and long-term relationship. 0-1 is established as permanent causality, while 2-3 is recognized as temporary causality. The (red) upper line and the (brown) lower line represent statistically significant levels of 5% and 10%, respectively. The (blue) curves are used for statistical tests of various interval frequencies (0, π). Variables' description is provided in Table 4 Gherghina and Simionescu Financial Innovation (2023) 9:21

Concluding remarks and policy implications
This paper examined whether daily changes in Bitcoin price react to COVID-19 pandemic news. The asymmetric volatility examination through EGARCH (1,1) model exhibited that adverse and optimistic news have the same effect, hence the FOMO behavior not being supported. By employing the NARDL framework, we reinforced prior literature (Rognone et al. 2020) and found positive and negative shocks in Rav-enPack coronavirus-related indices (Panic, Hype, Fake News, and Infodemic) stimulate Bitcoin returns; hence, during market instability, Bitcoin can withstand foreign shocks and act as a hedge. Additionally, we could argue that the cryptocurrency market seems resilient to the endless frictions brought on by the COVID-19 pandemic. Furthermore, we conclude that cryptocurrencies could be a crucial component of portfolio diversification. Moreover, in line with prior studies that used Twitter-based uncertainty measures (Wu et al. 2021b;Aharon et al. 2020), the outcomes of the Breitung-Candelon spectral Granger causality test reveals a one-way causality running from Coronavirus FNI and SI to Bitcoin returns, whereas Bitcoin price Granger cause Coronavirus PI and HI. Accordingly, Bitcoin might influence future investor behavior in the markets for virtual currencies.
Since the risk portfolios of worldwide investors and portfolio managers may be severely affected by the pandemic, acknowledging the conduct of digital currencies throughout times of intense tension, such as a COVID-19 pandemic and informed trading, is necessary. Therefore, investors can rely on RavenPack coronavirus-related indices as a significant driver of Bitcoin return and shape trading approaches accordingly. Understanding the connection between Bitcoin and panic can provide investors with insights for portfolio optimization or risk mitigation to deal with digital assets' price volatility. Therefore, investors should consider incorporating cryptocurrencies for their portfolios' optimization and diversification and use crypto assets for expenditures and fund transfers. Likewise, this research may be helpful to regulators and governments in developing policies to alleviate this market, lessen its significant instability, and boost investor trust. Authorities can assess the emotion-driven cryptocurrency crisis and take appropriate measures. As such, the government should enact appropriate legislation to guide the marketplace. Furthermore, authorities should supervise unethical strategies of cryptocurrency trading to assist economies in achieving economic security and investment gains.